Equivalence between Ampere and Grassmann´s forces

We calculate the force on part of a single closed circuit due to the remaining circuit in four different geometries according to the forces of Ampere and Grassmann. All analytical calculations are performed using surface or volume current elements in order to avoid the divergences which appear with linear current elements of zero diameter. We conclude that when we consider the action of a closed circuit as a whole and utilize only circuits with closed lines of current, there will be an equivalence between the expressions of Grassmann and Ampere. This means that both of them are compatible with the experimental findings related to Ampere´s bridge, contrary to the opinion of some authors